标签：百度 div style class img namespace clu for 线性
Problem Description
The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: suppose you are given a, b, try to calculate (a)+ (a+1)+....+ (b)
Input
There are several test cases. Each line has two integers a, b (2<a<b<3000000).
Output
Output the result of (a)+ (a+1)+....+ (b)
Sample Input
3 100
Sample Output
3042
Source
2009 Multi-University Training Contest 1 - Host by TJU
Recommend
gaojie
思路：
欧拉函数的定义：
φ(n)为小于n且与n互质的数的个数
欧拉函数有一个公式
其中pi为x的质因子，x不等于0
由此，可以用类似求素数的筛法
样例代码（来自百度百科）：
/*线性筛O(n)时间复杂度内筛出maxn内欧拉函数值*/ int m[maxn],phi[maxn],p[maxn],pt;//m[i]是i的最小素因数，p是素数，pt是素数个数 int make() { phi[1]=1; int N=maxn; int k; for(int i=2;i<N;i++) { if(!m[i])//i是素数 p[pt++]=m[i]=i,phi[i]=i-1; for(int j=0;j<pt&&(k=p[j]*i)<N;j++) { m[k]=p[j]; if(m[i]==p[j])//为了保证以后的数不被再筛，要break { phi[k]=phi[i]*p[j]; /*这里的phi[k]与phi[i]后面的∏(p[i]-1)/p[i]都一样（m[i]==p[j]）只差一个p[j]，就可以保证∏(p[i]-1)/p[i]前面也一样了*/ break; } else phi[k]=phi[i]*(p[j]-1);//积性函数性质，f(i*k)=f(i)*f(k) } } }
下面的是A题代码
#include<bits/stdc++.h> using namespace std; int ola[3000001];//存储欧拉函数的值 int prime[216817]; bool isprime[3000001]; int main() { __int64 n, a, b, i , j, k = 0; for(i = 2; i < 3000001; i++) { if(!isprime[i]) { ola[i] = i-1; prime[++k] = i; } for(j = 1; j <= k && prime[j]*i < 3000001; j++) { isprime[prime[j] * i] = 1; if(i % prime[j] == 0) { ola[prime[j]*i] = ola[i] * prime[j]; break; } else ola[prime[j] * i] = ola[i] * (prime[j]-1); } } while(cin >> a >> b) { __int64 ans = 0; while(a <= b) { ans += ola[a++]; } cout << ans << endl; } return 0; }
HDU2824--The Euler function（欧拉函数）
标签：百度 div style class img namespace clu for 线性
原文地址：http://www.cnblogs.com/liuzhanshan/p/6285713.html
